Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,10,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(12.8758959041\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.49740556.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 45x^{2} + 304 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.87724\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 41.3193 | 1.82607 | 0.913037 | − | 0.407877i | \(-0.133731\pi\) | ||||
0.913037 | + | 0.407877i | \(0.133731\pi\) | |||||||
\(3\) | 37.6407 | 0.268294 | 0.134147 | − | 0.990961i | \(-0.457170\pi\) | ||||
0.134147 | + | 0.990961i | \(0.457170\pi\) | |||||||
\(4\) | 1195.29 | 2.33455 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1555.29 | 0.489926 | ||||||||
\(7\) | 5315.22 | 0.836719 | 0.418360 | − | 0.908281i | \(-0.362605\pi\) | ||||
0.418360 | + | 0.908281i | \(0.362605\pi\) | |||||||
\(8\) | 28233.0 | 2.43698 | ||||||||
\(9\) | −18266.2 | −0.928018 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10426.2 | 0.214714 | 0.107357 | − | 0.994221i | \(-0.465761\pi\) | ||||
0.107357 | + | 0.994221i | \(0.465761\pi\) | |||||||
\(12\) | 44991.4 | 0.626346 | ||||||||
\(13\) | 79655.1 | 0.773515 | 0.386758 | − | 0.922181i | \(-0.373595\pi\) | ||||
0.386758 | + | 0.922181i | \(0.373595\pi\) | |||||||
\(14\) | 219621. | 1.52791 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 554581. | 2.11556 | ||||||||
\(17\) | −313750. | −0.911095 | −0.455547 | − | 0.890212i | \(-0.650556\pi\) | ||||
−0.455547 | + | 0.890212i | \(0.650556\pi\) | |||||||
\(18\) | −754746. | −1.69463 | ||||||||
\(19\) | −246945. | −0.434719 | −0.217360 | − | 0.976092i | \(-0.569744\pi\) | ||||
−0.217360 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 200068. | 0.224487 | ||||||||
\(22\) | 430806. | 0.392084 | ||||||||
\(23\) | −721761. | −0.537797 | −0.268898 | − | 0.963169i | \(-0.586660\pi\) | ||||
−0.268898 | + | 0.963169i | \(0.586660\pi\) | |||||||
\(24\) | 1.06271e6 | 0.653828 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.29130e6 | 1.41250 | ||||||||
\(27\) | −1.42843e6 | −0.517277 | ||||||||
\(28\) | 6.35321e6 | 1.95336 | ||||||||
\(29\) | 2.56903e6 | 0.674493 | 0.337247 | − | 0.941416i | \(-0.390504\pi\) | ||||
0.337247 | + | 0.941416i | \(0.390504\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.29543e6 | −0.640891 | −0.320445 | − | 0.947267i | \(-0.603833\pi\) | ||||
−0.320445 | + | 0.947267i | \(0.603833\pi\) | |||||||
\(32\) | 8.45965e6 | 1.42619 | ||||||||
\(33\) | 392451. | 0.0576066 | ||||||||
\(34\) | −1.29639e7 | −1.66373 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.18333e7 | −2.16650 | ||||||||
\(37\) | −1.40463e7 | −1.23212 | −0.616060 | − | 0.787699i | \(-0.711272\pi\) | ||||
−0.616060 | + | 0.787699i | \(0.711272\pi\) | |||||||
\(38\) | −1.02036e7 | −0.793830 | ||||||||
\(39\) | 2.99827e6 | 0.207530 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.70412e7 | 0.941830 | 0.470915 | − | 0.882178i | \(-0.343924\pi\) | ||||
0.470915 | + | 0.882178i | \(0.343924\pi\) | |||||||
\(42\) | 8.26669e6 | 0.409930 | ||||||||
\(43\) | −2.92261e7 | −1.30365 | −0.651827 | − | 0.758368i | \(-0.725997\pi\) | ||||
−0.651827 | + | 0.758368i | \(0.725997\pi\) | |||||||
\(44\) | 1.24624e7 | 0.501260 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.98227e7 | −0.982056 | ||||||||
\(47\) | −4.10316e7 | −1.22653 | −0.613264 | − | 0.789878i | \(-0.710144\pi\) | ||||
−0.613264 | + | 0.789878i | \(0.710144\pi\) | |||||||
\(48\) | 2.08748e7 | 0.567593 | ||||||||
\(49\) | −1.21021e7 | −0.299901 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.18098e7 | −0.244442 | ||||||||
\(52\) | 9.52108e7 | 1.80581 | ||||||||
\(53\) | 5.67230e7 | 0.987456 | 0.493728 | − | 0.869616i | \(-0.335634\pi\) | ||||
0.493728 | + | 0.869616i | \(0.335634\pi\) | |||||||
\(54\) | −5.90219e7 | −0.944585 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50065e8 | 2.03907 | ||||||||
\(57\) | −9.29518e6 | −0.116633 | ||||||||
\(58\) | 1.06150e8 | 1.23167 | ||||||||
\(59\) | 1.60408e8 | 1.72342 | 0.861710 | − | 0.507402i | \(-0.169394\pi\) | ||||
0.861710 | + | 0.507402i | \(0.169394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.33033e7 | 0.492912 | 0.246456 | − | 0.969154i | \(-0.420734\pi\) | ||||
0.246456 | + | 0.969154i | \(0.420734\pi\) | |||||||
\(62\) | −1.36165e8 | −1.17031 | ||||||||
\(63\) | −9.70887e7 | −0.776491 | ||||||||
\(64\) | 6.56012e7 | 0.488767 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.62158e7 | 0.105194 | ||||||||
\(67\) | 2.80916e8 | 1.70310 | 0.851548 | − | 0.524276i | \(-0.175664\pi\) | ||||
0.851548 | + | 0.524276i | \(0.175664\pi\) | |||||||
\(68\) | −3.75022e8 | −2.12699 | ||||||||
\(69\) | −2.71676e7 | −0.144288 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.97228e7 | −0.419025 | −0.209513 | − | 0.977806i | \(-0.567188\pi\) | ||||
−0.209513 | + | 0.977806i | \(0.567188\pi\) | |||||||
\(72\) | −5.15709e8 | −2.26156 | ||||||||
\(73\) | 7.60225e7 | 0.313321 | 0.156660 | − | 0.987653i | \(-0.449927\pi\) | ||||
0.156660 | + | 0.987653i | \(0.449927\pi\) | |||||||
\(74\) | −5.80383e8 | −2.24994 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.95170e8 | −1.01487 | ||||||||
\(77\) | 5.54178e7 | 0.179656 | ||||||||
\(78\) | 1.23887e8 | 0.378965 | ||||||||
\(79\) | 4.10672e8 | 1.18624 | 0.593120 | − | 0.805114i | \(-0.297896\pi\) | ||||
0.593120 | + | 0.805114i | \(0.297896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.05766e8 | 0.789236 | ||||||||
\(82\) | 7.04131e8 | 1.71985 | ||||||||
\(83\) | 5.21969e8 | 1.20724 | 0.603620 | − | 0.797272i | \(-0.293724\pi\) | ||||
0.603620 | + | 0.797272i | \(0.293724\pi\) | |||||||
\(84\) | 2.39139e8 | 0.524076 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.20760e9 | −2.38057 | ||||||||
\(87\) | 9.66999e7 | 0.180963 | ||||||||
\(88\) | 2.94364e8 | 0.523254 | ||||||||
\(89\) | 2.37312e8 | 0.400926 | 0.200463 | − | 0.979701i | \(-0.435755\pi\) | ||||
0.200463 | + | 0.979701i | \(0.435755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.23384e8 | 0.647215 | ||||||||
\(92\) | −8.62712e8 | −1.25551 | ||||||||
\(93\) | −1.24042e8 | −0.171947 | ||||||||
\(94\) | −1.69540e9 | −2.23973 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.18427e8 | 0.382639 | ||||||||
\(97\) | 6.03778e8 | 0.692476 | 0.346238 | − | 0.938147i | \(-0.387459\pi\) | ||||
0.346238 | + | 0.938147i | \(0.387459\pi\) | |||||||
\(98\) | −5.00050e8 | −0.547641 | ||||||||
\(99\) | −1.90448e8 | −0.199259 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.03606e8 | −0.194690 | −0.0973451 | − | 0.995251i | \(-0.531035\pi\) | ||||
−0.0973451 | + | 0.995251i | \(0.531035\pi\) | |||||||
\(102\) | −4.87972e8 | −0.446369 | ||||||||
\(103\) | −9.15893e8 | −0.801821 | −0.400910 | − | 0.916117i | \(-0.631306\pi\) | ||||
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(104\) | 2.24890e9 | 1.88504 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.34376e9 | 1.80317 | ||||||||
\(107\) | −1.66237e9 | −1.22603 | −0.613014 | − | 0.790072i | \(-0.710043\pi\) | ||||
−0.613014 | + | 0.790072i | \(0.710043\pi\) | |||||||
\(108\) | −1.70739e9 | −1.20761 | ||||||||
\(109\) | 1.73161e9 | 1.17498 | 0.587491 | − | 0.809231i | \(-0.300116\pi\) | ||||
0.587491 | + | 0.809231i | \(0.300116\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.28711e8 | −0.330571 | ||||||||
\(112\) | 2.94772e9 | 1.77013 | ||||||||
\(113\) | −6.30956e8 | −0.364038 | −0.182019 | − | 0.983295i | \(-0.558263\pi\) | ||||
−0.182019 | + | 0.983295i | \(0.558263\pi\) | |||||||
\(114\) | −3.84070e8 | −0.212980 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.07073e9 | 1.57464 | ||||||||
\(117\) | −1.45500e9 | −0.717836 | ||||||||
\(118\) | 6.62794e9 | 3.14709 | ||||||||
\(119\) | −1.66765e9 | −0.762331 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.24924e9 | −0.953898 | ||||||||
\(122\) | 2.20246e9 | 0.900094 | ||||||||
\(123\) | 6.41442e8 | 0.252688 | ||||||||
\(124\) | −3.93898e9 | −1.49619 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.01164e9 | −1.41793 | ||||||||
\(127\) | −2.12104e9 | −0.723490 | −0.361745 | − | 0.932277i | \(-0.617819\pi\) | ||||
−0.361745 | + | 0.932277i | \(0.617819\pi\) | |||||||
\(128\) | −1.62074e9 | −0.533664 | ||||||||
\(129\) | −1.10009e9 | −0.349763 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.57686e9 | 1.65451 | 0.827254 | − | 0.561828i | \(-0.189902\pi\) | ||||
0.827254 | + | 0.561828i | \(0.189902\pi\) | |||||||
\(132\) | 4.69092e8 | 0.134485 | ||||||||
\(133\) | −1.31257e9 | −0.363738 | ||||||||
\(134\) | 1.16072e10 | 3.10998 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.85810e9 | −2.22032 | ||||||||
\(137\) | 2.57317e9 | 0.624059 | 0.312029 | − | 0.950072i | \(-0.398991\pi\) | ||||
0.312029 | + | 0.950072i | \(0.398991\pi\) | |||||||
\(138\) | −1.12255e9 | −0.263480 | ||||||||
\(139\) | −1.62297e9 | −0.368761 | −0.184380 | − | 0.982855i | \(-0.559028\pi\) | ||||
−0.184380 | + | 0.982855i | \(0.559028\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.54446e9 | −0.329071 | ||||||||
\(142\) | −3.70729e9 | −0.765171 | ||||||||
\(143\) | 8.30504e8 | 0.166085 | ||||||||
\(144\) | −1.01301e10 | −1.96328 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.14120e9 | 0.572147 | ||||||||
\(147\) | −4.55530e8 | −0.0804617 | ||||||||
\(148\) | −1.67893e10 | −2.87644 | ||||||||
\(149\) | −5.98422e9 | −0.994647 | −0.497324 | − | 0.867565i | \(-0.665684\pi\) | ||||
−0.497324 | + | 0.867565i | \(0.665684\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.95089e9 | −0.931505 | −0.465753 | − | 0.884915i | \(-0.654216\pi\) | ||||
−0.465753 | + | 0.884915i | \(0.654216\pi\) | |||||||
\(152\) | −6.97200e9 | −1.05940 | ||||||||
\(153\) | 5.73101e9 | 0.845513 | ||||||||
\(154\) | 2.28983e9 | 0.328064 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3.58380e9 | 0.484488 | ||||||||
\(157\) | 2.94325e9 | 0.386615 | 0.193308 | − | 0.981138i | \(-0.438078\pi\) | ||||
0.193308 | + | 0.981138i | \(0.438078\pi\) | |||||||
\(158\) | 1.69687e10 | 2.16616 | ||||||||
\(159\) | 2.13509e9 | 0.264929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.83632e9 | −0.449985 | ||||||||
\(162\) | 1.26341e10 | 1.44120 | ||||||||
\(163\) | −2.69823e9 | −0.299389 | −0.149694 | − | 0.988732i | \(-0.547829\pi\) | ||||
−0.149694 | + | 0.988732i | \(0.547829\pi\) | |||||||
\(164\) | 2.03691e10 | 2.19875 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.15674e10 | 2.20451 | ||||||||
\(167\) | 1.47132e10 | 1.46380 | 0.731902 | − | 0.681410i | \(-0.238633\pi\) | ||||
0.731902 | + | 0.681410i | \(0.238633\pi\) | |||||||
\(168\) | 5.64853e9 | 0.547071 | ||||||||
\(169\) | −4.25956e9 | −0.401675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.51074e9 | 0.403427 | ||||||||
\(172\) | −3.49336e10 | −3.04344 | ||||||||
\(173\) | 1.56605e8 | 0.0132923 | 0.00664613 | − | 0.999978i | \(-0.497884\pi\) | ||||
0.00664613 | + | 0.999978i | \(0.497884\pi\) | |||||||
\(174\) | 3.99558e9 | 0.330452 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.78220e9 | 0.454241 | ||||||||
\(177\) | 6.03785e9 | 0.462384 | ||||||||
\(178\) | 9.80557e9 | 0.732121 | ||||||||
\(179\) | −5.35516e9 | −0.389883 | −0.194941 | − | 0.980815i | \(-0.562452\pi\) | ||||
−0.194941 | + | 0.980815i | \(0.562452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.52107e9 | −0.105341 | −0.0526704 | − | 0.998612i | \(-0.516773\pi\) | ||||
−0.0526704 | + | 0.998612i | \(0.516773\pi\) | |||||||
\(182\) | 1.74940e10 | 1.18186 | ||||||||
\(183\) | 2.00637e9 | 0.132246 | ||||||||
\(184\) | −2.03775e10 | −1.31060 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.12534e9 | −0.313989 | ||||||||
\(187\) | −3.27123e9 | −0.195625 | ||||||||
\(188\) | −4.90445e10 | −2.86339 | ||||||||
\(189\) | −7.59243e9 | −0.432815 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.28266e9 | −0.504687 | −0.252344 | − | 0.967638i | \(-0.581201\pi\) | ||||
−0.252344 | + | 0.967638i | \(0.581201\pi\) | |||||||
\(192\) | 2.46927e9 | 0.131134 | ||||||||
\(193\) | −6.94351e9 | −0.360223 | −0.180111 | − | 0.983646i | \(-0.557646\pi\) | ||||
−0.180111 | + | 0.983646i | \(0.557646\pi\) | |||||||
\(194\) | 2.49477e10 | 1.26451 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.44655e10 | −0.700132 | ||||||||
\(197\) | −3.60722e10 | −1.70637 | −0.853187 | − | 0.521606i | \(-0.825333\pi\) | ||||
−0.853187 | + | 0.521606i | \(0.825333\pi\) | |||||||
\(198\) | −7.86917e9 | −0.363861 | ||||||||
\(199\) | 2.25173e10 | 1.01784 | 0.508918 | − | 0.860815i | \(-0.330045\pi\) | ||||
0.508918 | + | 0.860815i | \(0.330045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.05739e10 | 0.456931 | ||||||||
\(202\) | −8.41286e9 | −0.355519 | ||||||||
\(203\) | 1.36549e10 | 0.564362 | ||||||||
\(204\) | −1.41161e10 | −0.570661 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.78441e10 | −1.46418 | ||||||||
\(207\) | 1.31838e10 | 0.499085 | ||||||||
\(208\) | 4.41753e10 | 1.63642 | ||||||||
\(209\) | −2.57471e9 | −0.0933404 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.62300e10 | 1.25834 | 0.629169 | − | 0.777268i | \(-0.283395\pi\) | ||||
0.629169 | + | 0.777268i | \(0.283395\pi\) | |||||||
\(212\) | 6.78003e10 | 2.30526 | ||||||||
\(213\) | −3.37723e9 | −0.112422 | ||||||||
\(214\) | −6.86879e10 | −2.23882 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.03289e10 | −1.26059 | ||||||||
\(217\) | −1.75159e10 | −0.536246 | ||||||||
\(218\) | 7.15490e10 | 2.14560 | ||||||||
\(219\) | 2.86154e9 | 0.0840623 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.49918e10 | −0.704746 | ||||||||
\(222\) | −2.18460e10 | −0.603647 | ||||||||
\(223\) | −4.93834e10 | −1.33724 | −0.668619 | − | 0.743605i | \(-0.733114\pi\) | ||||
−0.668619 | + | 0.743605i | \(0.733114\pi\) | |||||||
\(224\) | 4.49649e10 | 1.19332 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.60707e10 | −0.664760 | ||||||||
\(227\) | −3.27710e10 | −0.819169 | −0.409585 | − | 0.912272i | \(-0.634326\pi\) | ||||
−0.409585 | + | 0.912272i | \(0.634326\pi\) | |||||||
\(228\) | −1.11104e10 | −0.272285 | ||||||||
\(229\) | 1.35586e10 | 0.325803 | 0.162902 | − | 0.986642i | \(-0.447915\pi\) | ||||
0.162902 | + | 0.986642i | \(0.447915\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.08596e9 | 0.0482006 | ||||||||
\(232\) | 7.25313e10 | 1.64373 | ||||||||
\(233\) | 7.99837e9 | 0.177787 | 0.0888935 | − | 0.996041i | \(-0.471667\pi\) | ||||
0.0888935 | + | 0.996041i | \(0.471667\pi\) | |||||||
\(234\) | −6.01194e10 | −1.31082 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.91733e11 | 4.02340 | ||||||||
\(237\) | 1.54580e10 | 0.318262 | ||||||||
\(238\) | −6.89062e10 | −1.39207 | ||||||||
\(239\) | 8.30208e10 | 1.64587 | 0.822937 | − | 0.568133i | \(-0.192334\pi\) | ||||
0.822937 | + | 0.568133i | \(0.192334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.04789e10 | −1.15485 | −0.577427 | − | 0.816442i | \(-0.695943\pi\) | ||||
−0.577427 | + | 0.816442i | \(0.695943\pi\) | |||||||
\(242\) | −9.29372e10 | −1.74189 | ||||||||
\(243\) | 3.96251e10 | 0.729024 | ||||||||
\(244\) | 6.37128e10 | 1.15073 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.65040e10 | 0.461427 | ||||||||
\(247\) | −1.96704e10 | −0.336262 | ||||||||
\(248\) | −9.30398e10 | −1.56184 | ||||||||
\(249\) | 1.96473e10 | 0.323896 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.04682e11 | 1.66471 | 0.832354 | − | 0.554244i | \(-0.186993\pi\) | ||||
0.832354 | + | 0.554244i | \(0.186993\pi\) | |||||||
\(252\) | −1.16049e11 | −1.81275 | ||||||||
\(253\) | −7.52525e9 | −0.115473 | ||||||||
\(254\) | −8.76400e10 | −1.32115 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.00556e11 | −1.46328 | ||||||||
\(257\) | 7.92751e10 | 1.13354 | 0.566771 | − | 0.823875i | \(-0.308192\pi\) | ||||
0.566771 | + | 0.823875i | \(0.308192\pi\) | |||||||
\(258\) | −4.54549e10 | −0.638693 | ||||||||
\(259\) | −7.46590e10 | −1.03094 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.69263e10 | −0.625942 | ||||||||
\(262\) | 2.30432e11 | 3.02126 | ||||||||
\(263\) | 1.04629e8 | 0.00134850 | 0.000674250 | − | 1.00000i | \(-0.499785\pi\) | ||||
0.000674250 | 1.00000i | \(0.499785\pi\) | ||||||||
\(264\) | 1.10801e10 | 0.140386 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.42344e10 | −0.664213 | ||||||||
\(267\) | 8.93258e9 | 0.107566 | ||||||||
\(268\) | 3.35775e11 | 3.97596 | ||||||||
\(269\) | −7.38735e9 | −0.0860208 | −0.0430104 | − | 0.999075i | \(-0.513695\pi\) | ||||
−0.0430104 | + | 0.999075i | \(0.513695\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.27706e11 | 1.43831 | 0.719153 | − | 0.694852i | \(-0.244530\pi\) | ||||
0.719153 | + | 0.694852i | \(0.244530\pi\) | |||||||
\(272\) | −1.74000e11 | −1.92748 | ||||||||
\(273\) | 1.59365e10 | 0.173644 | ||||||||
\(274\) | 1.06322e11 | 1.13958 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.24731e10 | −0.336847 | ||||||||
\(277\) | 3.16563e10 | 0.323074 | 0.161537 | − | 0.986867i | \(-0.448355\pi\) | ||||
0.161537 | + | 0.986867i | \(0.448355\pi\) | |||||||
\(278\) | −6.70602e10 | −0.673385 | ||||||||
\(279\) | 6.01949e10 | 0.594758 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.50309e10 | −0.909257 | −0.454628 | − | 0.890681i | \(-0.650228\pi\) | ||||
−0.454628 | + | 0.890681i | \(0.650228\pi\) | |||||||
\(282\) | −6.38159e10 | −0.600908 | ||||||||
\(283\) | 4.91862e10 | 0.455832 | 0.227916 | − | 0.973681i | \(-0.426809\pi\) | ||||
0.227916 | + | 0.973681i | \(0.426809\pi\) | |||||||
\(284\) | −1.07245e11 | −0.978234 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.43159e10 | 0.303283 | ||||||||
\(287\) | 9.05777e10 | 0.788048 | ||||||||
\(288\) | −1.54525e11 | −1.32353 | ||||||||
\(289\) | −2.01488e10 | −0.169906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.27266e10 | 0.185787 | ||||||||
\(292\) | 9.08688e10 | 0.731462 | ||||||||
\(293\) | 3.53889e10 | 0.280519 | 0.140260 | − | 0.990115i | \(-0.455206\pi\) | ||||
0.140260 | + | 0.990115i | \(0.455206\pi\) | |||||||
\(294\) | −1.88222e10 | −0.146929 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.96568e11 | −3.00265 | ||||||||
\(297\) | −1.48932e10 | −0.111067 | ||||||||
\(298\) | −2.47264e11 | −1.81630 | ||||||||
\(299\) | −5.74920e10 | −0.415994 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.55343e11 | −1.09079 | ||||||||
\(302\) | −2.45887e11 | −1.70100 | ||||||||
\(303\) | −7.66386e9 | −0.0522343 | ||||||||
\(304\) | −1.36951e11 | −0.919675 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.36802e11 | 1.54397 | ||||||||
\(307\) | −8.30301e10 | −0.533474 | −0.266737 | − | 0.963769i | \(-0.585945\pi\) | ||||
−0.266737 | + | 0.963769i | \(0.585945\pi\) | |||||||
\(308\) | 6.62402e10 | 0.419414 | ||||||||
\(309\) | −3.44748e10 | −0.215124 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.13935e10 | 0.129676 | 0.0648382 | − | 0.997896i | \(-0.479347\pi\) | ||||
0.0648382 | + | 0.997896i | \(0.479347\pi\) | |||||||
\(312\) | 8.46502e10 | 0.505746 | ||||||||
\(313\) | −2.56558e11 | −1.51090 | −0.755452 | − | 0.655204i | \(-0.772582\pi\) | ||||
−0.755452 | + | 0.655204i | \(0.772582\pi\) | |||||||
\(314\) | 1.21613e11 | 0.705988 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.90871e11 | 2.76933 | ||||||||
\(317\) | 1.26112e11 | 0.701436 | 0.350718 | − | 0.936481i | \(-0.385938\pi\) | ||||
0.350718 | + | 0.936481i | \(0.385938\pi\) | |||||||
\(318\) | 8.82206e10 | 0.483780 | ||||||||
\(319\) | 2.67853e10 | 0.144823 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.25727e10 | −0.328936 | ||||||||
\(322\) | −1.58514e11 | −0.821706 | ||||||||
\(323\) | 7.74790e10 | 0.396071 | ||||||||
\(324\) | 3.65478e11 | 1.84251 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.11489e11 | −0.546706 | ||||||||
\(327\) | 6.51790e10 | 0.315241 | ||||||||
\(328\) | 4.81124e11 | 2.29522 | ||||||||
\(329\) | −2.18092e11 | −1.02626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.71300e11 | 0.784389 | 0.392194 | − | 0.919882i | \(-0.371716\pi\) | ||||
0.392194 | + | 0.919882i | \(0.371716\pi\) | |||||||
\(332\) | 6.23904e11 | 2.81836 | ||||||||
\(333\) | 2.56572e11 | 1.14343 | ||||||||
\(334\) | 6.07939e11 | 2.67301 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.10954e11 | 0.474916 | ||||||||
\(337\) | −4.70320e11 | −1.98637 | −0.993183 | − | 0.116569i | \(-0.962810\pi\) | ||||
−0.993183 | + | 0.116569i | \(0.962810\pi\) | |||||||
\(338\) | −1.76002e11 | −0.733487 | ||||||||
\(339\) | −2.37496e10 | −0.0976693 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.43589e10 | −0.137608 | ||||||||
\(342\) | 1.86381e11 | 0.736688 | ||||||||
\(343\) | −2.78813e11 | −1.08765 | ||||||||
\(344\) | −8.25140e11 | −3.17698 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.47083e9 | 0.0242727 | ||||||||
\(347\) | −2.86642e11 | −1.06135 | −0.530674 | − | 0.847576i | \(-0.678061\pi\) | ||||
−0.530674 | + | 0.847576i | \(0.678061\pi\) | |||||||
\(348\) | 1.15584e11 | 0.422466 | ||||||||
\(349\) | −3.54310e11 | −1.27841 | −0.639203 | − | 0.769038i | \(-0.720736\pi\) | ||||
−0.639203 | + | 0.769038i | \(0.720736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.13782e11 | −0.400121 | ||||||||
\(352\) | 8.82023e10 | 0.306223 | ||||||||
\(353\) | 2.09491e11 | 0.718092 | 0.359046 | − | 0.933320i | \(-0.383102\pi\) | ||||
0.359046 | + | 0.933320i | \(0.383102\pi\) | |||||||
\(354\) | 2.49480e11 | 0.844347 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.83656e11 | 0.935981 | ||||||||
\(357\) | −6.27715e10 | −0.204529 | ||||||||
\(358\) | −2.21272e11 | −0.711955 | ||||||||
\(359\) | 2.88081e11 | 0.915355 | 0.457678 | − | 0.889118i | \(-0.348681\pi\) | ||||
0.457678 | + | 0.889118i | \(0.348681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.61706e11 | −0.811019 | ||||||||
\(362\) | −6.28498e10 | −0.192360 | ||||||||
\(363\) | −8.46630e10 | −0.255926 | ||||||||
\(364\) | 5.06066e11 | 1.51095 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.29019e10 | 0.241490 | ||||||||
\(367\) | −1.33587e10 | −0.0384387 | −0.0192193 | − | 0.999815i | \(-0.506118\pi\) | ||||
−0.0192193 | + | 0.999815i | \(0.506118\pi\) | |||||||
\(368\) | −4.00275e11 | −1.13774 | ||||||||
\(369\) | −3.11278e11 | −0.874036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.01495e11 | 0.826224 | ||||||||
\(372\) | −1.48266e11 | −0.401419 | ||||||||
\(373\) | −4.17763e11 | −1.11748 | −0.558741 | − | 0.829342i | \(-0.688716\pi\) | ||||
−0.558741 | + | 0.829342i | \(0.688716\pi\) | |||||||
\(374\) | −1.35165e11 | −0.357226 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.15844e12 | −2.98903 | ||||||||
\(377\) | 2.04636e11 | 0.521731 | ||||||||
\(378\) | −3.13714e11 | −0.790353 | ||||||||
\(379\) | 2.63110e11 | 0.655031 | 0.327515 | − | 0.944846i | \(-0.393789\pi\) | ||||
0.327515 | + | 0.944846i | \(0.393789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.98374e10 | −0.194108 | ||||||||
\(382\) | −3.83553e11 | −0.921596 | ||||||||
\(383\) | 7.84146e10 | 0.186210 | 0.0931049 | − | 0.995656i | \(-0.470321\pi\) | ||||
0.0931049 | + | 0.995656i | \(0.470321\pi\) | |||||||
\(384\) | −6.10057e10 | −0.143179 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.86901e11 | −0.657793 | ||||||||
\(387\) | 5.33849e11 | 1.20981 | ||||||||
\(388\) | 7.21688e11 | 1.61662 | ||||||||
\(389\) | 1.66007e11 | 0.367581 | 0.183791 | − | 0.982965i | \(-0.441163\pi\) | ||||
0.183791 | + | 0.982965i | \(0.441163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.26452e11 | 0.489984 | ||||||||
\(392\) | −3.41678e11 | −0.730852 | ||||||||
\(393\) | 2.09917e11 | 0.443896 | ||||||||
\(394\) | −1.49048e12 | −3.11596 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.27640e11 | −0.465179 | ||||||||
\(397\) | 4.09536e11 | 0.827437 | 0.413719 | − | 0.910405i | \(-0.364230\pi\) | ||||
0.413719 | + | 0.910405i | \(0.364230\pi\) | |||||||
\(398\) | 9.30402e11 | 1.85865 | ||||||||
\(399\) | −4.94059e10 | −0.0975889 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.92645e10 | −0.153084 | −0.0765419 | − | 0.997066i | \(-0.524388\pi\) | ||||
−0.0765419 | + | 0.997066i | \(0.524388\pi\) | |||||||
\(402\) | 4.36905e11 | 0.834391 | ||||||||
\(403\) | −2.62498e11 | −0.495739 | ||||||||
\(404\) | −2.43367e11 | −0.454513 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.64213e11 | 1.03057 | ||||||||
\(407\) | −1.46450e11 | −0.264554 | ||||||||
\(408\) | −3.33425e11 | −0.595700 | ||||||||
\(409\) | 6.85827e11 | 1.21188 | 0.605940 | − | 0.795510i | \(-0.292797\pi\) | ||||
0.605940 | + | 0.795510i | \(0.292797\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.68557e10 | 0.167431 | ||||||||
\(412\) | −1.09476e12 | −1.87189 | ||||||||
\(413\) | 8.52601e11 | 1.44202 | ||||||||
\(414\) | 5.44746e11 | 0.911366 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.73854e11 | 1.10318 | ||||||||
\(417\) | −6.10898e10 | −0.0989365 | ||||||||
\(418\) | −1.06385e11 | −0.170447 | ||||||||
\(419\) | 3.31879e11 | 0.526037 | 0.263018 | − | 0.964791i | \(-0.415282\pi\) | ||||
0.263018 | + | 0.964791i | \(0.415282\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.30694e11 | −0.978475 | −0.489237 | − | 0.872151i | \(-0.662725\pi\) | ||||
−0.489237 | + | 0.872151i | \(0.662725\pi\) | |||||||
\(422\) | 1.49700e12 | 2.29782 | ||||||||
\(423\) | 7.49490e11 | 1.13824 | ||||||||
\(424\) | 1.60146e12 | 2.40641 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.39545e11 | −0.205291 | ||||||||
\(427\) | 2.83319e11 | 0.412429 | ||||||||
\(428\) | −1.98701e12 | −2.86222 | ||||||||
\(429\) | 3.12607e10 | 0.0445596 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.70903e11 | 1.07610 | 0.538049 | − | 0.842913i | \(-0.319161\pi\) | ||||
0.538049 | + | 0.842913i | \(0.319161\pi\) | |||||||
\(432\) | −7.92182e11 | −1.09433 | ||||||||
\(433\) | −1.07829e12 | −1.47415 | −0.737075 | − | 0.675811i | \(-0.763794\pi\) | ||||
−0.737075 | + | 0.675811i | \(0.763794\pi\) | |||||||
\(434\) | −7.23746e11 | −0.979225 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.06977e12 | 2.74305 | ||||||||
\(437\) | 1.78235e11 | 0.233791 | ||||||||
\(438\) | 1.18237e11 | 0.153504 | ||||||||
\(439\) | −9.56419e11 | −1.22902 | −0.614508 | − | 0.788910i | \(-0.710646\pi\) | ||||
−0.614508 | + | 0.788910i | \(0.710646\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.21059e11 | 0.278313 | ||||||||
\(442\) | −1.03264e12 | −1.28692 | ||||||||
\(443\) | −2.06392e11 | −0.254611 | −0.127305 | − | 0.991864i | \(-0.540633\pi\) | ||||
−0.127305 | + | 0.991864i | \(0.540633\pi\) | |||||||
\(444\) | −6.31962e11 | −0.771734 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.04049e12 | −2.44190 | ||||||||
\(447\) | −2.25250e11 | −0.266858 | ||||||||
\(448\) | 3.48685e11 | 0.408961 | ||||||||
\(449\) | 1.75939e11 | 0.204293 | 0.102147 | − | 0.994769i | \(-0.467429\pi\) | ||||
0.102147 | + | 0.994769i | \(0.467429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.77676e11 | 0.202224 | ||||||||
\(452\) | −7.54174e11 | −0.849863 | ||||||||
\(453\) | −2.23995e11 | −0.249918 | ||||||||
\(454\) | −1.35408e12 | −1.49586 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.62431e11 | −0.284232 | ||||||||
\(457\) | 2.98819e11 | 0.320469 | 0.160234 | − | 0.987079i | \(-0.448775\pi\) | ||||
0.160234 | + | 0.987079i | \(0.448775\pi\) | |||||||
\(458\) | 5.60233e11 | 0.594941 | ||||||||
\(459\) | 4.48171e11 | 0.471288 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.39422e11 | 0.453135 | 0.226567 | − | 0.973995i | \(-0.427250\pi\) | ||||
0.226567 | + | 0.973995i | \(0.427250\pi\) | |||||||
\(462\) | 8.61906e10 | 0.0880179 | ||||||||
\(463\) | 1.16254e12 | 1.17569 | 0.587846 | − | 0.808973i | \(-0.299976\pi\) | ||||
0.587846 | + | 0.808973i | \(0.299976\pi\) | |||||||
\(464\) | 1.42473e12 | 1.42693 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.30487e11 | 0.324652 | ||||||||
\(467\) | 1.65923e11 | 0.161429 | 0.0807144 | − | 0.996737i | \(-0.474280\pi\) | ||||
0.0807144 | + | 0.996737i | \(0.474280\pi\) | |||||||
\(468\) | −1.73914e12 | −1.67582 | ||||||||
\(469\) | 1.49313e12 | 1.42501 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.10786e11 | 0.103727 | ||||||||
\(472\) | 4.52879e12 | 4.19994 | ||||||||
\(473\) | −3.04718e11 | −0.279913 | ||||||||
\(474\) | 6.38712e11 | 0.581169 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.99332e12 | −1.77970 | ||||||||
\(477\) | −1.03611e12 | −0.916377 | ||||||||
\(478\) | 3.43036e12 | 3.00549 | ||||||||
\(479\) | 1.33180e11 | 0.115592 | 0.0577960 | − | 0.998328i | \(-0.481593\pi\) | ||||
0.0577960 | + | 0.998328i | \(0.481593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.11886e12 | −0.953064 | ||||||||
\(482\) | −2.49895e12 | −2.10885 | ||||||||
\(483\) | −1.44401e11 | −0.120728 | ||||||||
\(484\) | −2.68849e12 | −2.22692 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.63728e12 | 1.33125 | ||||||||
\(487\) | −1.43276e12 | −1.15423 | −0.577116 | − | 0.816662i | \(-0.695822\pi\) | ||||
−0.577116 | + | 0.816662i | \(0.695822\pi\) | |||||||
\(488\) | 1.50491e12 | 1.20122 | ||||||||
\(489\) | −1.01563e11 | −0.0803243 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.05688e12 | −0.820655 | −0.410327 | − | 0.911938i | \(-0.634586\pi\) | ||||
−0.410327 | + | 0.911938i | \(0.634586\pi\) | |||||||
\(492\) | 7.66708e11 | 0.589912 | ||||||||
\(493\) | −8.06032e11 | −0.614527 | ||||||||
\(494\) | −8.12769e11 | −0.614039 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.82758e12 | −1.35584 | ||||||||
\(497\) | −4.76896e11 | −0.350607 | ||||||||
\(498\) | 8.11813e11 | 0.591458 | ||||||||
\(499\) | 1.77897e11 | 0.128445 | 0.0642223 | − | 0.997936i | \(-0.479543\pi\) | ||||
0.0642223 | + | 0.997936i | \(0.479543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.53814e11 | 0.392730 | ||||||||
\(502\) | 4.32537e12 | 3.03988 | ||||||||
\(503\) | −1.58467e12 | −1.10378 | −0.551889 | − | 0.833917i | \(-0.686093\pi\) | ||||
−0.551889 | + | 0.833917i | \(0.686093\pi\) | |||||||
\(504\) | −2.74111e12 | −1.89229 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.10939e11 | −0.210861 | ||||||||
\(507\) | −1.60333e11 | −0.107767 | ||||||||
\(508\) | −2.53525e12 | −1.68902 | ||||||||
\(509\) | −1.93674e12 | −1.27891 | −0.639456 | − | 0.768827i | \(-0.720841\pi\) | ||||
−0.639456 | + | 0.768827i | \(0.720841\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.04076e11 | 0.262162 | ||||||||
\(512\) | −3.32508e12 | −2.13839 | ||||||||
\(513\) | 3.52744e11 | 0.224870 | ||||||||
\(514\) | 3.27560e12 | 2.06993 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.31492e12 | −0.816538 | ||||||||
\(517\) | −4.27805e11 | −0.263353 | ||||||||
\(518\) | −3.08486e12 | −1.88257 | ||||||||
\(519\) | 5.89473e9 | 0.00356624 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.72419e12 | 1.61982 | 0.809912 | − | 0.586552i | \(-0.199515\pi\) | ||||
0.809912 | + | 0.586552i | \(0.199515\pi\) | |||||||
\(522\) | −1.93896e12 | −1.14302 | ||||||||
\(523\) | −4.86784e11 | −0.284497 | −0.142249 | − | 0.989831i | \(-0.545433\pi\) | ||||
−0.142249 | + | 0.989831i | \(0.545433\pi\) | |||||||
\(524\) | 6.66596e12 | 3.86253 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.32320e9 | 0.00246246 | ||||||||
\(527\) | 1.03394e12 | 0.583912 | ||||||||
\(528\) | 2.17646e11 | 0.121870 | ||||||||
\(529\) | −1.28021e12 | −0.710775 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.93003e12 | −1.59936 | ||||||||
\(532\) | −1.56889e12 | −0.849164 | ||||||||
\(533\) | 1.35742e12 | 0.728520 | ||||||||
\(534\) | 3.69088e11 | 0.196424 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 7.93109e12 | 4.15041 | ||||||||
\(537\) | −2.01572e11 | −0.104603 | ||||||||
\(538\) | −3.05240e11 | −0.157080 | ||||||||
\(539\) | −1.26179e11 | −0.0643929 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.98233e11 | 0.0994920 | 0.0497460 | − | 0.998762i | \(-0.484159\pi\) | ||||
0.0497460 | + | 0.998762i | \(0.484159\pi\) | |||||||
\(542\) | 5.27675e12 | 2.62645 | ||||||||
\(543\) | −5.72543e10 | −0.0282624 | ||||||||
\(544\) | −2.65421e12 | −1.29939 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.58485e11 | 0.317087 | ||||||||
\(547\) | 4.79532e11 | 0.229021 | 0.114510 | − | 0.993422i | \(-0.463470\pi\) | ||||
0.114510 | + | 0.993422i | \(0.463470\pi\) | |||||||
\(548\) | 3.07567e12 | 1.45689 | ||||||||
\(549\) | −9.73647e11 | −0.457432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.34408e11 | −0.293215 | ||||||||
\(552\) | −7.67022e11 | −0.351627 | ||||||||
\(553\) | 2.18281e12 | 0.992550 | ||||||||
\(554\) | 1.30802e12 | 0.589957 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.93992e12 | −0.860889 | ||||||||
\(557\) | −1.20856e11 | −0.0532011 | −0.0266006 | − | 0.999646i | \(-0.508468\pi\) | ||||
−0.0266006 | + | 0.999646i | \(0.508468\pi\) | |||||||
\(558\) | 2.48721e12 | 1.08607 | ||||||||
\(559\) | −2.32801e12 | −1.00840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.23131e11 | −0.0524851 | ||||||||
\(562\) | −3.92662e12 | −1.66037 | ||||||||
\(563\) | 1.01468e12 | 0.425637 | 0.212818 | − | 0.977092i | \(-0.431736\pi\) | ||||
0.212818 | + | 0.977092i | \(0.431736\pi\) | |||||||
\(564\) | −1.84607e12 | −0.768231 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.03234e12 | 0.832382 | ||||||||
\(567\) | 1.62521e12 | 0.660369 | ||||||||
\(568\) | −2.53314e12 | −1.02116 | ||||||||
\(569\) | 1.12630e12 | 0.450454 | 0.225227 | − | 0.974306i | \(-0.427688\pi\) | ||||
0.225227 | + | 0.974306i | \(0.427688\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.75478e12 | −1.08449 | −0.542243 | − | 0.840221i | \(-0.682425\pi\) | ||||
−0.542243 | + | 0.840221i | \(0.682425\pi\) | |||||||
\(572\) | 9.92691e11 | 0.387732 | ||||||||
\(573\) | −3.49405e11 | −0.135405 | ||||||||
\(574\) | 3.74261e12 | 1.43903 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.19828e12 | −0.453585 | ||||||||
\(577\) | 4.14763e12 | 1.55779 | 0.778895 | − | 0.627155i | \(-0.215781\pi\) | ||||
0.778895 | + | 0.627155i | \(0.215781\pi\) | |||||||
\(578\) | −8.32535e11 | −0.310261 | ||||||||
\(579\) | −2.61358e11 | −0.0966458 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.77438e12 | 1.01012 | ||||||||
\(582\) | 9.39049e11 | 0.339262 | ||||||||
\(583\) | 5.91408e11 | 0.212021 | ||||||||
\(584\) | 2.14634e12 | 0.763557 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.46224e12 | 0.512248 | ||||||||
\(587\) | 1.38017e12 | 0.479800 | 0.239900 | − | 0.970798i | \(-0.422885\pi\) | ||||
0.239900 | + | 0.970798i | \(0.422885\pi\) | |||||||
\(588\) | −5.44490e11 | −0.187842 | ||||||||
\(589\) | 8.13789e11 | 0.278608 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.35778e12 | −0.457811 | ||||||||
\(592\) | −7.78980e12 | −2.60663 | ||||||||
\(593\) | −6.90406e11 | −0.229276 | −0.114638 | − | 0.993407i | \(-0.536571\pi\) | ||||
−0.114638 | + | 0.993407i | \(0.536571\pi\) | |||||||
\(594\) | −6.15377e11 | −0.202816 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.15286e12 | −2.32205 | ||||||||
\(597\) | 8.47568e11 | 0.273080 | ||||||||
\(598\) | −2.37553e12 | −0.759635 | ||||||||
\(599\) | 1.24239e12 | 0.394309 | 0.197155 | − | 0.980372i | \(-0.436830\pi\) | ||||
0.197155 | + | 0.980372i | \(0.436830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.01140e12 | 0.628873 | 0.314437 | − | 0.949278i | \(-0.398184\pi\) | ||||
0.314437 | + | 0.949278i | \(0.398184\pi\) | |||||||
\(602\) | −6.41867e12 | −1.99187 | ||||||||
\(603\) | −5.13126e12 | −1.58050 | ||||||||
\(604\) | −7.11302e12 | −2.17464 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.16666e11 | −0.0953837 | ||||||||
\(607\) | −2.73579e12 | −0.817963 | −0.408981 | − | 0.912543i | \(-0.634116\pi\) | ||||
−0.408981 | + | 0.912543i | \(0.634116\pi\) | |||||||
\(608\) | −2.08907e12 | −0.619992 | ||||||||
\(609\) | 5.13981e11 | 0.151415 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.26838e12 | −0.948738 | ||||||||
\(612\) | 6.85021e12 | 1.97389 | ||||||||
\(613\) | 1.63707e12 | 0.468269 | 0.234135 | − | 0.972204i | \(-0.424774\pi\) | ||||
0.234135 | + | 0.972204i | \(0.424774\pi\) | |||||||
\(614\) | −3.43075e12 | −0.974162 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.56461e12 | 0.437817 | ||||||||
\(617\) | −1.22267e12 | −0.339646 | −0.169823 | − | 0.985475i | \(-0.554320\pi\) | ||||
−0.169823 | + | 0.985475i | \(0.554320\pi\) | |||||||
\(618\) | −1.42448e12 | −0.392832 | ||||||||
\(619\) | −5.78784e12 | −1.58456 | −0.792280 | − | 0.610158i | \(-0.791106\pi\) | ||||
−0.792280 | + | 0.610158i | \(0.791106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.03099e12 | 0.278190 | ||||||||
\(622\) | 8.83967e11 | 0.236799 | ||||||||
\(623\) | 1.26136e12 | 0.335463 | ||||||||
\(624\) | 1.66279e12 | 0.439042 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.06008e13 | −2.75902 | ||||||||
\(627\) | −9.69138e10 | −0.0250427 | ||||||||
\(628\) | 3.51803e12 | 0.902571 | ||||||||
\(629\) | 4.40702e12 | 1.12258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00341e12 | 0.503081 | 0.251540 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251540 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(632\) | 1.15945e13 | 2.89084 | ||||||||
\(633\) | 1.36372e12 | 0.337605 | ||||||||
\(634\) | 5.21084e12 | 1.28087 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.55205e12 | 0.618489 | ||||||||
\(637\) | −9.63992e11 | −0.231978 | ||||||||
\(638\) | 1.10675e12 | 0.264458 | ||||||||
\(639\) | 1.63889e12 | 0.388863 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.75478e12 | 0.644505 | 0.322253 | − | 0.946654i | \(-0.395560\pi\) | ||||
0.322253 | + | 0.946654i | \(0.395560\pi\) | |||||||
\(642\) | −2.58546e12 | −0.600662 | ||||||||
\(643\) | 7.38857e12 | 1.70455 | 0.852277 | − | 0.523091i | \(-0.175221\pi\) | ||||
0.852277 | + | 0.523091i | \(0.175221\pi\) | |||||||
\(644\) | −4.58550e12 | −1.05051 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.20138e12 | 0.723254 | ||||||||
\(647\) | −4.12045e12 | −0.924432 | −0.462216 | − | 0.886767i | \(-0.652946\pi\) | ||||
−0.462216 | + | 0.886767i | \(0.652946\pi\) | |||||||
\(648\) | 8.63269e12 | 1.92335 | ||||||||
\(649\) | 1.67245e12 | 0.370043 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.59311e11 | −0.143872 | ||||||||
\(652\) | −3.22517e12 | −0.698937 | ||||||||
\(653\) | −6.51407e12 | −1.40198 | −0.700992 | − | 0.713170i | \(-0.747259\pi\) | ||||
−0.700992 | + | 0.713170i | \(0.747259\pi\) | |||||||
\(654\) | 2.69315e12 | 0.575654 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.45073e12 | 1.99250 | ||||||||
\(657\) | −1.38864e12 | −0.290767 | ||||||||
\(658\) | −9.01141e12 | −1.87403 | ||||||||
\(659\) | −1.74145e12 | −0.359688 | −0.179844 | − | 0.983695i | \(-0.557559\pi\) | ||||
−0.179844 | + | 0.983695i | \(0.557559\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.39849e12 | −0.284939 | −0.142469 | − | 0.989799i | \(-0.545504\pi\) | ||||
−0.142469 | + | 0.989799i | \(0.545504\pi\) | |||||||
\(662\) | 7.07800e12 | 1.43235 | ||||||||
\(663\) | −9.40708e11 | −0.189079 | ||||||||
\(664\) | 1.47368e13 | 2.94202 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.06014e13 | 2.08799 | ||||||||
\(667\) | −1.85422e12 | −0.362740 | ||||||||
\(668\) | 1.75865e13 | 3.41732 | ||||||||
\(669\) | −1.85882e12 | −0.358774 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.55753e11 | 0.105835 | ||||||||
\(672\) | 1.69251e12 | 0.320161 | ||||||||
\(673\) | −7.23077e12 | −1.35868 | −0.679340 | − | 0.733824i | \(-0.737734\pi\) | ||||
−0.679340 | + | 0.733824i | \(0.737734\pi\) | |||||||
\(674\) | −1.94333e13 | −3.62725 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.09140e12 | −0.937728 | ||||||||
\(677\) | −1.09854e12 | −0.200986 | −0.100493 | − | 0.994938i | \(-0.532042\pi\) | ||||
−0.100493 | + | 0.994938i | \(0.532042\pi\) | |||||||
\(678\) | −9.81319e11 | −0.178351 | ||||||||
\(679\) | 3.20921e12 | 0.579408 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.23352e12 | −0.219779 | ||||||||
\(682\) | −1.41969e12 | −0.251283 | ||||||||
\(683\) | −1.51781e12 | −0.266885 | −0.133442 | − | 0.991057i | \(-0.542603\pi\) | ||||
−0.133442 | + | 0.991057i | \(0.542603\pi\) | |||||||
\(684\) | 5.39163e12 | 0.941820 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.15204e13 | −1.98613 | ||||||||
\(687\) | 5.10355e11 | 0.0874112 | ||||||||
\(688\) | −1.62082e13 | −2.75796 | ||||||||
\(689\) | 4.51828e12 | 0.763812 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.51489e12 | 0.252772 | 0.126386 | − | 0.991981i | \(-0.459662\pi\) | ||||
0.126386 | + | 0.991981i | \(0.459662\pi\) | |||||||
\(692\) | 1.87188e11 | 0.0310314 | ||||||||
\(693\) | −1.01227e12 | −0.166724 | ||||||||
\(694\) | −1.18439e13 | −1.93810 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.73013e12 | 0.441003 | ||||||||
\(697\) | −5.34668e12 | −0.858097 | ||||||||
\(698\) | −1.46398e13 | −2.33446 | ||||||||
\(699\) | 3.01064e11 | 0.0476993 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.62368e12 | 1.19243 | 0.596216 | − | 0.802824i | \(-0.296670\pi\) | ||||
0.596216 | + | 0.802824i | \(0.296670\pi\) | |||||||
\(702\) | −4.70140e12 | −0.730651 | ||||||||
\(703\) | 3.46866e12 | 0.535627 | ||||||||
\(704\) | 6.83975e11 | 0.104945 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.65605e12 | 1.31129 | ||||||||
\(707\) | −1.08221e12 | −0.162901 | ||||||||
\(708\) | 7.21697e12 | 1.07946 | ||||||||
\(709\) | 1.00657e13 | 1.49602 | 0.748010 | − | 0.663687i | \(-0.231009\pi\) | ||||
0.748010 | + | 0.663687i | \(0.231009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.50140e12 | −1.10085 | ||||||||
\(712\) | 6.70002e12 | 0.977049 | ||||||||
\(713\) | 2.37851e12 | 0.344669 | ||||||||
\(714\) | −2.59367e12 | −0.373485 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.40096e12 | −0.910199 | ||||||||
\(717\) | 3.12496e12 | 0.441579 | ||||||||
\(718\) | 1.19033e13 | 1.67151 | ||||||||
\(719\) | 8.94464e12 | 1.24820 | 0.624098 | − | 0.781346i | \(-0.285466\pi\) | ||||
0.624098 | + | 0.781346i | \(0.285466\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.86817e12 | −0.670899 | ||||||||
\(722\) | −1.08135e13 | −1.48098 | ||||||||
\(723\) | −2.27647e12 | −0.309841 | ||||||||
\(724\) | −1.81812e12 | −0.245923 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.49822e12 | −0.467339 | ||||||||
\(727\) | 1.22168e13 | 1.62201 | 0.811006 | − | 0.585038i | \(-0.198921\pi\) | ||||
0.811006 | + | 0.585038i | \(0.198921\pi\) | |||||||
\(728\) | 1.19534e13 | 1.57725 | ||||||||
\(729\) | −4.52688e12 | −0.593642 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.16968e12 | 1.18775 | ||||||||
\(732\) | 2.39819e12 | 0.308734 | ||||||||
\(733\) | 1.44452e13 | 1.84823 | 0.924114 | − | 0.382118i | \(-0.124805\pi\) | ||||
0.924114 | + | 0.382118i | \(0.124805\pi\) | |||||||
\(734\) | −5.51974e11 | −0.0701919 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.10584e12 | −0.767000 | ||||||||
\(737\) | 2.92889e12 | 0.365679 | ||||||||
\(738\) | −1.28618e13 | −1.59605 | ||||||||
\(739\) | −1.11591e13 | −1.37635 | −0.688175 | − | 0.725545i | \(-0.741588\pi\) | ||||
−0.688175 | + | 0.725545i | \(0.741588\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.40409e11 | −0.0902172 | ||||||||
\(742\) | 1.24576e13 | 1.50875 | ||||||||
\(743\) | −9.35882e12 | −1.12660 | −0.563302 | − | 0.826251i | \(-0.690469\pi\) | ||||
−0.563302 | + | 0.826251i | \(0.690469\pi\) | |||||||
\(744\) | −3.50208e12 | −0.419033 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.72617e13 | −2.04061 | ||||||||
\(747\) | −9.53439e12 | −1.12034 | ||||||||
\(748\) | −3.91007e12 | −0.456696 | ||||||||
\(749\) | −8.83585e12 | −1.02584 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.28609e13 | −1.47533 | −0.737667 | − | 0.675165i | \(-0.764072\pi\) | ||||
−0.737667 | + | 0.675165i | \(0.764072\pi\) | |||||||
\(752\) | −2.27553e13 | −2.59480 | ||||||||
\(753\) | 3.94028e12 | 0.446632 | ||||||||
\(754\) | 8.45543e12 | 0.952719 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.07514e12 | −1.01043 | ||||||||
\(757\) | 1.42250e13 | 1.57442 | 0.787211 | − | 0.616684i | \(-0.211524\pi\) | ||||
0.787211 | + | 0.616684i | \(0.211524\pi\) | |||||||
\(758\) | 1.08716e13 | 1.19613 | ||||||||
\(759\) | −2.83256e11 | −0.0309807 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.65722e13 | 1.79122 | 0.895610 | − | 0.444841i | \(-0.146740\pi\) | ||||
0.895610 | + | 0.444841i | \(0.146740\pi\) | |||||||
\(762\) | −3.29883e12 | −0.354456 | ||||||||
\(763\) | 9.20389e12 | 0.983130 | ||||||||
\(764\) | −1.10954e13 | −1.17822 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.24004e12 | 0.340033 | ||||||||
\(767\) | 1.27773e13 | 1.33309 | ||||||||
\(768\) | −3.78498e12 | −0.392589 | ||||||||
\(769\) | 2.81269e12 | 0.290037 | 0.145019 | − | 0.989429i | \(-0.453676\pi\) | ||||
0.145019 | + | 0.989429i | \(0.453676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.98397e12 | 0.304123 | ||||||||
\(772\) | −8.29949e12 | −0.840957 | ||||||||
\(773\) | −8.57982e12 | −0.864311 | −0.432156 | − | 0.901799i | \(-0.642247\pi\) | ||||
−0.432156 | + | 0.901799i | \(0.642247\pi\) | |||||||
\(774\) | 2.20583e13 | 2.20921 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.70465e13 | 1.68755 | ||||||||
\(777\) | −2.81021e12 | −0.276595 | ||||||||
\(778\) | 6.85930e12 | 0.671230 | ||||||||
\(779\) | −4.20824e12 | −0.409432 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.35472e11 | −0.0899707 | ||||||||
\(782\) | 9.35687e12 | 0.894746 | ||||||||
\(783\) | −3.66968e12 | −0.348900 | ||||||||
\(784\) | −6.71158e12 | −0.634458 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 8.67363e12 | 0.810586 | ||||||||
\(787\) | −1.75771e12 | −0.163328 | −0.0816642 | − | 0.996660i | \(-0.526024\pi\) | ||||
−0.0816642 | + | 0.996660i | \(0.526024\pi\) | |||||||
\(788\) | −4.31166e13 | −3.98361 | ||||||||
\(789\) | 3.93830e9 | 0.000361795 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.35367e12 | −0.304597 | ||||||||
\(792\) | −5.37691e12 | −0.485590 | ||||||||
\(793\) | 4.24588e12 | 0.381275 | ||||||||
\(794\) | 1.69218e13 | 1.51096 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.69147e13 | 2.37619 | ||||||||
\(797\) | −2.27115e13 | −1.99381 | −0.996905 | − | 0.0786130i | \(-0.974951\pi\) | ||||
−0.996905 | + | 0.0786130i | \(0.974951\pi\) | |||||||
\(798\) | −2.04142e12 | −0.178205 | ||||||||
\(799\) | 1.28737e13 | 1.11748 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.33478e12 | −0.372067 | ||||||||
\(802\) | −3.27516e12 | −0.279542 | ||||||||
\(803\) | 7.92629e11 | 0.0672744 | ||||||||
\(804\) | 1.26388e13 | 1.06673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.08462e13 | −0.905255 | ||||||||
\(807\) | −2.78065e11 | −0.0230789 | ||||||||
\(808\) | −5.74840e12 | −0.474456 | ||||||||
\(809\) | −9.95176e12 | −0.816829 | −0.408415 | − | 0.912796i | \(-0.633918\pi\) | ||||
−0.408415 | + | 0.912796i | \(0.633918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.01292e12 | −0.569253 | −0.284626 | − | 0.958639i | \(-0.591870\pi\) | ||||
−0.284626 | + | 0.958639i | \(0.591870\pi\) | |||||||
\(812\) | 1.63216e13 | 1.31753 | ||||||||
\(813\) | 4.80696e12 | 0.385889 | ||||||||
\(814\) | −6.05121e12 | −0.483095 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.54948e12 | −0.517131 | ||||||||
\(817\) | 7.21723e12 | 0.566724 | ||||||||
\(818\) | 2.83379e13 | 2.21298 | ||||||||
\(819\) | −7.73362e12 | −0.600627 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.20992e13 | −0.929420 | −0.464710 | − | 0.885463i | \(-0.653841\pi\) | ||||
−0.464710 | + | 0.885463i | \(0.653841\pi\) | |||||||
\(822\) | 4.00202e12 | 0.305742 | ||||||||
\(823\) | −1.21261e13 | −0.921346 | −0.460673 | − | 0.887570i | \(-0.652392\pi\) | ||||
−0.460673 | + | 0.887570i | \(0.652392\pi\) | |||||||
\(824\) | −2.58584e13 | −1.95402 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.52289e13 | 2.63323 | ||||||||
\(827\) | 1.32495e13 | 0.984973 | 0.492486 | − | 0.870320i | \(-0.336088\pi\) | ||||
0.492486 | + | 0.870320i | \(0.336088\pi\) | |||||||
\(828\) | 1.57584e13 | 1.16514 | ||||||||
\(829\) | −1.87106e13 | −1.37592 | −0.687960 | − | 0.725749i | \(-0.741493\pi\) | ||||
−0.687960 | + | 0.725749i | \(0.741493\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.19157e12 | 0.0866789 | ||||||||
\(832\) | 5.22548e12 | 0.378069 | ||||||||
\(833\) | 3.79702e12 | 0.273238 | ||||||||
\(834\) | −2.52419e12 | −0.180665 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.07752e12 | −0.217908 | ||||||||
\(837\) | 4.70730e12 | 0.331518 | ||||||||
\(838\) | 1.37130e13 | 0.960582 | ||||||||
\(839\) | 1.21346e13 | 0.845469 | 0.422734 | − | 0.906254i | \(-0.361070\pi\) | ||||
0.422734 | + | 0.906254i | \(0.361070\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.90725e12 | −0.545059 | ||||||||
\(842\) | −2.60599e13 | −1.78677 | ||||||||
\(843\) | −3.57703e12 | −0.243949 | ||||||||
\(844\) | 4.33053e13 | 2.93765 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.09684e13 | 2.07851 | ||||||||
\(847\) | −1.19552e13 | −0.798145 | ||||||||
\(848\) | 3.14575e13 | 2.08902 | ||||||||
\(849\) | 1.85140e12 | 0.122297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.01380e13 | 0.662630 | ||||||||
\(852\) | −4.03676e12 | −0.262455 | ||||||||
\(853\) | −2.34098e13 | −1.51401 | −0.757004 | − | 0.653411i | \(-0.773337\pi\) | ||||
−0.757004 | + | 0.653411i | \(0.773337\pi\) | |||||||
\(854\) | 1.17065e13 | 0.753126 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.69336e13 | −2.98780 | ||||||||
\(857\) | −1.61008e13 | −1.01961 | −0.509805 | − | 0.860290i | \(-0.670282\pi\) | ||||
−0.509805 | + | 0.860290i | \(0.670282\pi\) | |||||||
\(858\) | 1.29167e12 | 0.0813691 | ||||||||
\(859\) | −1.34163e13 | −0.840745 | −0.420373 | − | 0.907352i | \(-0.638101\pi\) | ||||
−0.420373 | + | 0.907352i | \(0.638101\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.40940e12 | 0.211429 | ||||||||
\(862\) | 3.18532e13 | 1.96504 | ||||||||
\(863\) | 2.03784e13 | 1.25061 | 0.625304 | − | 0.780381i | \(-0.284975\pi\) | ||||
0.625304 | + | 0.780381i | \(0.284975\pi\) | |||||||
\(864\) | −1.20840e13 | −0.737735 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.45544e13 | −2.69191 | ||||||||
\(867\) | −7.58415e11 | −0.0455849 | ||||||||
\(868\) | −2.09366e13 | −1.25189 | ||||||||
\(869\) | 4.28176e12 | 0.254703 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.23764e13 | 1.31737 | ||||||||
\(872\) | 4.88886e13 | 2.86341 | ||||||||
\(873\) | −1.10287e13 | −0.642630 | ||||||||
\(874\) | 7.36456e12 | 0.426919 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.42036e12 | 0.196247 | ||||||||
\(877\) | −3.55027e12 | −0.202658 | −0.101329 | − | 0.994853i | \(-0.532309\pi\) | ||||
−0.101329 | + | 0.994853i | \(0.532309\pi\) | |||||||
\(878\) | −3.95186e13 | −2.24428 | ||||||||
\(879\) | 1.33206e12 | 0.0752617 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.33443e13 | −1.30554 | −0.652769 | − | 0.757557i | \(-0.726393\pi\) | ||||
−0.652769 | + | 0.757557i | \(0.726393\pi\) | |||||||
\(882\) | 9.13399e12 | 0.508220 | ||||||||
\(883\) | 8.70030e12 | 0.481627 | 0.240814 | − | 0.970571i | \(-0.422586\pi\) | ||||
0.240814 | + | 0.970571i | \(0.422586\pi\) | |||||||
\(884\) | −2.98724e13 | −1.64526 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.52799e12 | −0.464938 | ||||||||
\(887\) | −2.98568e13 | −1.61952 | −0.809761 | − | 0.586760i | \(-0.800403\pi\) | ||||
−0.809761 | + | 0.586760i | \(0.800403\pi\) | |||||||
\(888\) | −1.49271e13 | −0.805596 | ||||||||
\(889\) | −1.12738e13 | −0.605358 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.18799e12 | 0.169460 | ||||||||
\(892\) | −5.90273e13 | −3.12184 | ||||||||
\(893\) | 1.01325e13 | 0.533196 | ||||||||
\(894\) | −9.30718e12 | −0.487303 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.61458e12 | −0.446527 | ||||||||
\(897\) | −2.16404e12 | −0.111609 | ||||||||
\(898\) | 7.26969e12 | 0.373055 | ||||||||
\(899\) | −8.46604e12 | −0.432277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.77968e13 | −0.899666 | ||||||||
\(902\) | 7.34144e12 | 0.369277 | ||||||||
\(903\) | −5.84721e12 | −0.292654 | ||||||||
\(904\) | −1.78138e13 | −0.887153 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.25534e12 | −0.456368 | ||||||||
\(907\) | −2.14293e13 | −1.05142 | −0.525709 | − | 0.850664i | \(-0.676200\pi\) | ||||
−0.525709 | + | 0.850664i | \(0.676200\pi\) | |||||||
\(908\) | −3.91708e13 | −1.91239 | ||||||||
\(909\) | 3.71910e12 | 0.180676 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.43474e13 | 1.65219 | 0.826097 | − | 0.563529i | \(-0.190557\pi\) | ||||
0.826097 | + | 0.563529i | \(0.190557\pi\) | |||||||
\(912\) | −5.15493e12 | −0.246744 | ||||||||
\(913\) | 5.44218e12 | 0.259212 | ||||||||
\(914\) | 1.23470e13 | 0.585200 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.62064e13 | 0.760603 | ||||||||
\(917\) | 2.96422e13 | 1.38436 | ||||||||
\(918\) | 1.85181e13 | 0.860607 | ||||||||
\(919\) | 2.05847e13 | 0.951975 | 0.475987 | − | 0.879452i | \(-0.342091\pi\) | ||||
0.475987 | + | 0.879452i | \(0.342091\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.12531e12 | −0.143128 | ||||||||
\(922\) | 1.81566e13 | 0.827458 | ||||||||
\(923\) | −7.14688e12 | −0.324122 | ||||||||
\(924\) | 2.49332e12 | 0.112527 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.80354e13 | 2.14690 | ||||||||
\(927\) | 1.67299e13 | 0.744104 | ||||||||
\(928\) | 2.17331e13 | 0.961955 | ||||||||
\(929\) | 1.78605e13 | 0.786726 | 0.393363 | − | 0.919383i | \(-0.371312\pi\) | ||||
0.393363 | + | 0.919383i | \(0.371312\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.98855e12 | 0.130373 | ||||||||
\(932\) | 9.56035e12 | 0.415052 | ||||||||
\(933\) | 8.05267e11 | 0.0347915 | ||||||||
\(934\) | 6.85583e12 | 0.294781 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.10789e13 | −1.74935 | ||||||||
\(937\) | 1.00969e13 | 0.427917 | 0.213959 | − | 0.976843i | \(-0.431364\pi\) | ||||
0.213959 | + | 0.976843i | \(0.431364\pi\) | |||||||
\(938\) | 6.16950e13 | 2.60218 | ||||||||
\(939\) | −9.65703e12 | −0.405367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.40159e12 | −0.0998496 | −0.0499248 | − | 0.998753i | \(-0.515898\pi\) | ||||
−0.0499248 | + | 0.998753i | \(0.515898\pi\) | |||||||
\(942\) | 4.57760e12 | 0.189413 | ||||||||
\(943\) | −1.22997e13 | −0.506513 | ||||||||
\(944\) | 8.89591e13 | 3.64600 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.25908e13 | −0.511142 | ||||||||
\(947\) | 2.09609e13 | 0.846907 | 0.423453 | − | 0.905918i | \(-0.360818\pi\) | ||||
0.423453 | + | 0.905918i | \(0.360818\pi\) | |||||||
\(948\) | 1.84767e13 | 0.742997 | ||||||||
\(949\) | 6.05558e12 | 0.242358 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.74692e12 | 0.188191 | ||||||||
\(952\) | −4.70827e13 | −1.85779 | ||||||||
\(953\) | 1.23636e12 | 0.0485543 | 0.0242771 | − | 0.999705i | \(-0.492272\pi\) | ||||
0.0242771 | + | 0.999705i | \(0.492272\pi\) | |||||||
\(954\) | −4.28115e13 | −1.67337 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 9.92338e13 | 3.84237 | ||||||||
\(957\) | 1.00822e12 | 0.0388553 | ||||||||
\(958\) | 5.50289e12 | 0.211080 | ||||||||
\(959\) | 1.36769e13 | 0.522162 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.55798e13 | −0.589259 | ||||||||
\(962\) | −4.62305e13 | −1.74037 | ||||||||
\(963\) | 3.03651e13 | 1.13778 | ||||||||
\(964\) | −7.22897e13 | −2.69606 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.96657e12 | −0.220459 | ||||||||
\(967\) | 1.93044e13 | 0.709966 | 0.354983 | − | 0.934873i | \(-0.384487\pi\) | ||||
0.354983 | + | 0.934873i | \(0.384487\pi\) | |||||||
\(968\) | −6.35028e13 | −2.32463 | ||||||||
\(969\) | 2.91636e12 | 0.106264 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.95198e12 | −0.106568 | −0.0532840 | − | 0.998579i | \(-0.516969\pi\) | ||||
−0.0532840 | + | 0.998579i | \(0.516969\pi\) | |||||||
\(972\) | 4.73634e13 | 1.70194 | ||||||||
\(973\) | −8.62646e12 | −0.308549 | ||||||||
\(974\) | −5.92007e13 | −2.10771 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.95610e13 | 1.04279 | ||||||||
\(977\) | 5.39705e13 | 1.89509 | 0.947547 | − | 0.319617i | \(-0.103554\pi\) | ||||
0.947547 | + | 0.319617i | \(0.103554\pi\) | |||||||
\(978\) | −4.19653e12 | −0.146678 | ||||||||
\(979\) | 2.47427e12 | 0.0860845 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.16299e13 | −1.09040 | ||||||||
\(982\) | −4.36697e13 | −1.49858 | ||||||||
\(983\) | 2.52782e13 | 0.863487 | 0.431743 | − | 0.901996i | \(-0.357899\pi\) | ||||
0.431743 | + | 0.901996i | \(0.357899\pi\) | |||||||
\(984\) | 1.81098e13 | 0.615795 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.33047e13 | −1.12217 | ||||||||
\(987\) | −8.20912e12 | −0.275340 | ||||||||
\(988\) | −2.35118e13 | −0.785019 | ||||||||
\(989\) | 2.10942e13 | 0.701101 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.62973e13 | 1.19548 | 0.597741 | − | 0.801689i | \(-0.296065\pi\) | ||||
0.597741 | + | 0.801689i | \(0.296065\pi\) | |||||||
\(992\) | −2.78781e13 | −0.914032 | ||||||||
\(993\) | 6.44785e12 | 0.210447 | ||||||||
\(994\) | −1.97050e13 | −0.640234 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.34842e13 | 0.756150 | ||||||||
\(997\) | −5.75313e13 | −1.84406 | −0.922032 | − | 0.387114i | \(-0.873472\pi\) | ||||
−0.922032 | + | 0.387114i | \(0.873472\pi\) | |||||||
\(998\) | 7.35058e12 | 0.234549 | ||||||||
\(999\) | 2.00642e13 | 0.637347 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 25.10.a.e.1.4 | 4 | ||
3.2 | odd | 2 | 225.10.a.s.1.1 | 4 | |||
4.3 | odd | 2 | 400.10.a.ba.1.2 | 4 | |||
5.2 | odd | 4 | 5.10.b.a.4.4 | yes | 4 | ||
5.3 | odd | 4 | 5.10.b.a.4.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 25.10.a.e.1.1 | 4 | ||
15.2 | even | 4 | 45.10.b.b.19.1 | 4 | |||
15.8 | even | 4 | 45.10.b.b.19.4 | 4 | |||
15.14 | odd | 2 | 225.10.a.s.1.4 | 4 | |||
20.3 | even | 4 | 80.10.c.c.49.2 | 4 | |||
20.7 | even | 4 | 80.10.c.c.49.3 | 4 | |||
20.19 | odd | 2 | 400.10.a.ba.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.10.b.a.4.1 | ✓ | 4 | 5.3 | odd | 4 | ||
5.10.b.a.4.4 | yes | 4 | 5.2 | odd | 4 | ||
25.10.a.e.1.1 | 4 | 5.4 | even | 2 | inner | ||
25.10.a.e.1.4 | 4 | 1.1 | even | 1 | trivial | ||
45.10.b.b.19.1 | 4 | 15.2 | even | 4 | |||
45.10.b.b.19.4 | 4 | 15.8 | even | 4 | |||
80.10.c.c.49.2 | 4 | 20.3 | even | 4 | |||
80.10.c.c.49.3 | 4 | 20.7 | even | 4 | |||
225.10.a.s.1.1 | 4 | 3.2 | odd | 2 | |||
225.10.a.s.1.4 | 4 | 15.14 | odd | 2 | |||
400.10.a.ba.1.2 | 4 | 4.3 | odd | 2 | |||
400.10.a.ba.1.3 | 4 | 20.19 | odd | 2 |